Existence criteria for Landau-Pekar polarons

We build the distribution function for a system with coexisting self-locali zed and delocalized fermions. The distribution function is used to study th e behavior of the chemical potential of the carriers in such a system, whic h is found to differ substantially from the behavior of the chemical potent ial in a system of delocalized fermions. We also find that as the temperatu re changes, isostructural first-order phase transitions can emerge in the s ystem of self-localized and delocalized fermions. These transitions, for wh ich changes in the state of the macroscopic number of particles are respons ible, manifest themselves in the electrical conductivity, in the contributi on of carriers to the specific heat, and in the optical properties of such systems. Formulas are derived that approximate the dependence of the temper ature of such a phase transition on the binding energy of the self-localize d states of carriers and on the maximum group velocity of phonons participa ting in the formation of such states. Finally, we show that the special fea tures of the behavior of the chemical potential of the carriers in a system with carrier self-localization lead to the possibility of Bose condensatio n in a system where bipolaron states are metastable. (C) 1999 American Inst itute of Physics. [S1063-7761(99)01910-1].